9 papers
Subadditivity of shifts, Eilenberg-Zilber shuffle products and homology of lattices
Karim Adiprasito, Anders Björner, Joel Hakavuori +2
We show that the maximal shifts in the minimal free resolution of the quotients of a polynomial ring by a monomial ideal are subadditive as a function of the homological degree. Th…
Homological algebra and poset versions of the Garland method
Eric Babson, Volkmar Welker
Garland introduced a vanishing criterion for a characteristic zero cohomology group of a locally finite and locally connected simplicial complex. The criterion is based on the spec…
Generalized binomial edge ideals are Cartwright-Sturmfels
Aldo Conca, Emanuela De Negri, Volkmar Welker
Binomial edge ideals associated to a simple graph G were introduced by Herzog and collaborators and, independently, by Ohtani. They became an ``instant classic" in combinatorial co…
Posets of decompositions in spherical buildings
Kevin Ivan Piterman, John Shareshian, Volkmar Welker
We propose definitions of the common bases complex, the poset of decompositions, and the poset of partial decompositions for arbitrary spherical buildings. We show that the poset o…
On the homology of simplicial and cubical sets with symmetries
Curtis Greene, Volkmar Welker, Georg Wille
We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. W…
Notes on the topology of independence structures
Kevin Ivan Piterman, Volkmar Welker
Following Welsh, a pre-independence space (pi-space) is a set together with a non-empty collection of subsets of , called independent sets, which is closed under taki…